A Hybrid Nonlinear Predictor: Analysis of Learning Process and Predictability for Noisy Time Series

摘要

A nonlinear time series predictor was proposed, in which a nonlinear sub-predictor (NSP) and a linear sub- predictor (LSP) are combined in a cascade form. This model is called "hybrid predictor" here. The nonlinearity analysis method of the input time series was also proposed to estimate the net- work size. We have considered the nonlinear prediction problem as a pattern mapping one. A multi-layer neural network, which consists of sigmoidal hidden neurons and a single linear output neuron, has been employed as a nonlinear sub-predictor. Since the NSP includes nonlinear functions, it can predict the nonlin- earity of the input time series. However, the prediction is not complete in some cases. Therefore, the NSP prediction error is further compensated for by employing a linear sub-predictor af ter the NSP. In this paper, the prediction mechanism and a role of the NSP and the LSP are theoretically and experimentally an- alyzed. The role of the NSP is to predict the nonlinear and some part of the linear property of the time series. The LSP works to predict the NSP prediction error. Furthermore, predictabil- ity of the hybrid predictor for noisy time series is investigated. The sigmoidal functions used in the NSP can suppress the noise effects by using their saturation regions. Computer simulations, using several kinds of nonlinear time series and other conventional predictor models, are demonstrated. The theoretical analysis of the predictor mechanism is confirmed through these simulations. Furthermore, predictability is improved by slightly expanding or shifting the input pot